I'd like to discuss about how you go about hitting a 'pro' serve

Not just them rec lollipops . I haven't really been able to play matches in a while and it seems I've lost my old serve. Rather than try and recover it, I figured since it was the reason I injured my elbow in the first place, I should go and really work on improving it.

Basically I have a couple of questions:
*How are you supposed to swing the racket? Like do you swing using your elbow or your shoulder or something else?
*How does pronation come into play? i.e. is it manually done or not?
*What does fed/sampras do different that makes their serve way better than nadal/agassi?
*Other key points that you think I should address

Please try and dumb it down as much as possible to only the very basic essentials required to hit a good quality (aka 'pro') serve. Thanks in advance.

The serve is a complicated movement. It's often compared to throwing a ball high over your head. There are plenty of youtube vids that break down the motion, but the key is you have to have a very relaxed arm and wrist. It's kind of like driving a golf ball. The minute you start trying to hit it hard, your motion will fall apart.

The best way to understand pronation is to face a tall fence and swing up to it. Then practice easy serves with a choked up grip from the service line.

The most important pro serve is probably the kick serve - unless you are over 6'5 or so. Federer, Djokovic, Nadal and many other players use it as their normal serve on first and second serves. Not necessarily a kick serve which jumps 6' in the air, but most pros have a lot of spin on their serves as it improves percentages and makes the shot harder to judge for the opponent.

Having a serve that is very dependable for you, but hard to predict for your opponent, is very helpful in higher pressure situations.

Lots of questions, but in the modern era, your best bet is to go to the video and watch good servers and then video yourself and attempt to mimic them.

The best servers are doing a relaxed throwing type motion but designed to accelerate a racket head rather than throw a ball. The racket acts as a big lever so that is why things like pronation make sense (though many will quibble and say it is mostly internal shoulder rotation, which it may well be). Use a continental grip and don't hit the serve with the racket handle in line with your forearm, there needs to be an angle. This will necessitate the pronation/internal rotation move. It all happens very quickly, so it is a result of both swing path and muscle firing, but the best servers are probably just thinking about a target as everything else is drilled.

Unless someone writes a novel, I don't think they can tell you all the steps to hitting a good serve here, but ideas and concepts that may help:
1. study video on serve basics - anything on yourtube by "the serve doctor" is really good as he is the serve coach at Boliterie's. Serve doctors stuff about hitting up the mountain, and using a throwing motion are very good. Also, fuzzy yellow balls video on basic, slice and kick serve is good.
2. Throwing drills where you throw a ball upward thru the contact zone and then visualize throwing the racket head up are excellent
3. understanding that spin is critical to serving - unless you are 6'3" or over, I would forget about "flat" serves and think hard top/slice serves instead. Simple physics say if the ball does not bend in the air, it isn't going into the box for all but the very tallest players. Sampras hit over 2,000 rpm on his 1st serve
4. think loose motion and fast motion but learn to serve with a loose grip, relaxed hands, wrist, arms, and shoulders. Muscling the ball deters from speed as tense muscles slow down instead of speed up. Also, a flowing, relaxed swing can be repeated when you are tired - watch video of Federer or old video of Pancho Gonzalez for smooth, flowing serves that can be repeated when tired. Gonzalez served huge into his forties because he was tall and had such a fluid motion.